文[1]用均值不等式巧妙的证明命题1,文[2]给出了文[1]的一个变式,得到命题2,本文在两篇文章的基础上给出一个进一步的推广.命题1已知正数p,q满足p~3+q~3=2,求证:p+q≤2.命题2已知正数p,q满足p~n+q~n=2,求证:p+q≤2.(n∈N) In [1], we use the mean inequality to subtly prove Proposition 1, and [2] gives a variant of [1] to get Proposition 2. This paper gives a further generalization on the basis of two articles. Proposition 1 Known positive numbers p, q to meet p~3+q~3=2, verification: p+q≤2. Proposition 2 Known positive number p, q satisfies p~n+q~n=2, Proof: p+q≤ 2.(n∈N)